Development of support vector machine-based model and comparative analysis with artificial neural network for modeling the plant tissue culture procedures: Effect of plant growth regulators on somatic embryogenesis of chrysanthemum, as a case study

Abstract

Background
Optimizing the somatic embryogenesis protocol can be considered as the first and foremost step in successful gene transformation studies. However, it is usually difficult to achieve an optimized embryogenesis protocol due to the cost and time-consuming as well as the complexity of this process. Therefore, it is necessary to use a novel computational approach, such as machine learning algorithms for this aim. In the present study, two machine learning algorithms, including Multilayer Perceptron (MLP) as an artificial neural network (ANN) and support vector regression (SVR), were employed to model somatic embryogenesis of chrysanthemum, as a case study, and compare their prediction accuracy.

Results
The results showed that SVR (R2 > 0.92) had better performance accuracy than MLP (R2 > 0.82). Moreover, the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) was also applied for the optimization of the somatic embryogenesis and the results showed that the highest embryogenesis rate (99.09%) and the maximum number of somatic embryos per explant (56.24) can be obtained from a medium containing 9.10 μM 2,4-dichlorophenoxyacetic acid (2,4-D), 4.70 μM kinetin (KIN), and 18.73 μM sodium nitroprusside (SNP). According to our results, SVR-NSGA-II was able to optimize the chrysanthemum’s somatic embryogenesis accurately.

Conclusions
SVR-NSGA-II can be employed as a reliable and applicable computational methodology in future plant tissue culture studies.

Full text

Hesamietal. Plant Methods (2020) 16:112
https://doi.org/10.1186/s13007-020-00655-9
RESEARCH
Development ofsupport vector
machine-based model andcomparative analysis
witharticial neural network formodeling
theplant tissue culture procedures: eect
ofplant growth regulators onsomatic
embryogenesis ofchrysanthemum, asacase
study
Mohsen Hesami1, Roohangiz Naderi2* , Masoud Tohidfar3 and Mohsen Yoosefzadeh‑Najafabadi1
Abstract
Background: Optimizing the somatic embryogenesis protocol can be considered as the first and foremost step in
successful gene transformation studies. However, it is usually difficult to achieve an optimized embryogenesis proto‑
col due to the cost and time‑consuming as well as the complexity of this process. Therefore, it is necessary to use a
novel computational approach, such as machine learning algorithms for this aim. In the present study, two machine
learning algorithms, including Multilayer Perceptron (MLP) as an artificial neural network (ANN) and support vector
regression (SVR), were employed to model somatic embryogenesis of chrysanthemum, as a case study, and compare
their prediction accuracy.
Results: The results showed that SVR (R2 > 0.92) had better performance accuracy than MLP (R2 > 0.82). Moreover, the
Non‑dominated Sorting Genetic Algorithm‑II (NSGA‑II) was also applied for the optimization of the somatic embryo‑
genesis and the results showed that the highest embryogenesis rate (99.09%) and the maximum number of somatic
embryos per explant (56.24) can be obtained from a medium containing 9.10 μM 2,4‑dichlorophenoxyacetic acid
(2,4‑D), 4.70 μM kinetin (KIN), and 18.73 μM sodium nitroprusside (SNP). According to our results, SVR‑NSGA‑II was able
to optimize the chrysanthemum’s somatic embryogenesis accurately.
Conclusions: SVR‑NSGA‑II can be employed as a reliable and applicable computational methodology in future plant
tissue culture studies.
Keywords: Artificial intelligence, Support vector regression, Multi‑objective optimization algorithm, Machine
learning algorithms, Multilayer perceptron, Somatic embryogenesis, Chrysanthemum, Nitric oxide
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Background
Chrysanthemum (Dendranthema × grandiflorum) can be
categorized as one of the most economically important
ornamental species due to its color and morphological
Open Access
Plant Methods
*Correspondence: rnaderi@ut.ac.ir
2 Department of Horticultural Science, Faculty of Agriculture, University
of Tehran, Karaj, Iran
Full list of author information is available at the end of the article
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Hesamietal. Plant Methods (2020) 16:112
diversity. Moreover, chrysanthemum has been used as a
model plant for color modification studies [1–3]. Con-
ventional propagation and breeding approaches are not
able to meet the increasing demands of the market for
this valuable ornamental plant. erefore, novel bio-
technological methods can be employed in order to sat-
isfy the demands of consumers [1, 3]. Nowadays, invitro
culture methods as biotechnological tools are applied to
the rapid multiplication of rare plant genotypes, micro-
propagation of disease-free plants, production of plant-
derived metabolites, and gene transformation [1, 3–5].
To study invitro functional genomics, somatic embryos
have been employed as a potential explant material [2,
3, 6, 7]. Moreover, many studies proved the usefulness
of embryogenesis as a comprehensive model in study-
ing plant growth and development [6, 8, 9]. e unique
developmental pathway represented by somatic embry-
ogenesis can be categorized in different characteristic
events such as cell differentiation, activation of cell divi-
sion, dedifferentiation of cells and reprogramming of
their metabolism, gene expression patterns, and physiol-
ogy [9]. us, efficient somatic embryogenesis protocol
can play a conspicuous role in successful chrysanthemum
genetic manipulation and regeneration. Using the appro-
priate type and concentration of plant growth regula-
tors (PGRs) in various combinations could improve the
somatic embryogenesis of different plant species and
explants [10–12]. Indeed, invitro embryogenesis is con-
trolled by the balances of exogenous PGRs and concen-
trations of endogenous phytohormones. e levels of
endogenous phytohormones regulate the invitro explant
differentiation and are assumed to be the major variation
sources between different genotypes and explants [1, 13–
17]. erefore, optimizing the somatic embryogenesis
protocol can be considered as the first and foremost step
in successful gene transformation studies. However, it is
usually difficult to achieve an optimized embryogenesis
protocol because it is a laborious, time-consuming, and
complex process. erefore, it is necessary to use a novel
computational approach for addressing this bottleneck.
In vitro culture consists of highly complex and nonlin-
ear processes such as dedifferentiation, re-differentiation,
or differentiation due to the genetic and environmental
factors [18–21]. erefore, it would be difficult to pre-
dict different in vitro culture parameters such as cal-
logenesis rate, embryogenesis rate, and the number of
somatic embryos as well as optimize factors involved in
these parameters by simple conventional mathematical
methods [22–24]. Furthermore, biological processes such
as somatic embryogenesis cannot be described as a sim-
ple stepwise algorithm, especially when the datasets are
highly noisy and complex [25–29]. erefore, machine
learning algorithms can be employed as an efficient and
reliable computational methodology to interpret and pre-
dict different unpredictable datasets [30–34]. Recently,
Multilayer Perceptron (MLP) as one of the common arti-
ficial neural networks (ANNs) has been widely employed
for modeling and predicting invitro culture systems such
as invitro sterilization [35, 36], callogenesis [37–39], cell
growth and protoplast culture [40, 41], somatic embry-
ogenesis [38, 42, 43], shoot regeneration [25, 44–46],
androgenesis [47], hairy root culture [48, 49], and invitro
rooting and acclimatization [31]. MLP is a type of non-
linear computational methods, which can be applied for
different aims such as clustering, predicting, and classify-
ing the complex systems [47, 50]. MLP is able to identify
the relationship between output and input variables and
recognize the inherent knowledge existent in the datasets
without previous physical considerations [29, 51]. is
algorithm consists of numerous highly interconnected
processing neurons that work in parallel to find a solu-
tion for a particular problem. MLP is learned by exam-
ple, which should be carefully chosen otherwise time is
wasted or even in worse scenarios, the model might be
working inaccurately [52].
Support vector machines (SVMs), developed by Vapnik
[53], are a kind of interesting, powerful, and easy to inter-
pret machine learning algorithms that analyze data and
recognize patterns, used for clustering, classification and
regression analysis of nonlinear relationships [54]. Some
of the advantages of SVMs in comparison with MLP are
related to the complexity of the networks; MLP usually
implementing very small number of hidden neurons,
whereas SVM uses a large number of hidden units. e
best advantage of SVMs is the formulation of the learn-
ing problem, resulting in the quadratic optimization task
[55, 56]. Support Vector Regression (SVR) is a regression
version of SVM. Recently, several studies were published
regarding SVM-based approaches in solving industrially
or chemically important problems [57–59]. However,
SVR, unlike MLP, is relatively unknown to scientists in
the field of plant tissue culture. Also, there is no com-
prehensive study to compare MLP with other machine
learning algorithms (e.g. SVR) in order to develop an
appropriate model for predicting invitro culture param-
eters such as callogenesis rate, embryogenesis rate, and
number of somatic embryos.
Different studies [25, 28, 30, 31, 34] have widely
employed evolutionary optimization algorithms, in
particular, genetic algorithm (GA) as a single optimiza-
tion algorithm to optimize different factors involved in
invitro culture parameters. is common single-objec-
tive optimization algorithm offers merit points over
more conventional optimization methods [60, 61]. Also,
GA has the benefit that it does not need initial estimates
for the decision variables. However, GA can be just
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Hesamietal. Plant Methods (2020) 16:112
employed for a single objective function. On the other
hand, the Non-dominated Sorting Genetic Algorithm
(NSGA) developed by Srinivas and Deb [62] has been
successfully employed to optimize many multi-objective
variables. However, the main disadvantage of NSGA has
been the lack of elitism, the requirements for specifying
sharing parameters, and its high computational com-
plexity of non-dominated sorting [60]. NSGA-II is the
improved version of NSGA, which has a better incorpo-
rates elitism, sorting algorithm, and no sharing parameter
requires to be chosen a priori [35]. erefore, the elitist
NSGA-II can be utilized for multi-objective optimization
with two, three, or more objective functions [7]. Recently,
NSGA-II has been successfully applied to optimize shoot
regeneration rate, number of shoots, and callus weight,
simultaneously [33].
In the current study, SVR has been employed to pre-
dict the somatic embryogenesis parameters, including
callogenesis rate, embryogenesis rate, and the number
of somatic embryos of chrysanthemum. e developed
SVR-based model was compared with MLP in terms of
statistical performance parameters to find the most suit-
able model for modeling and predicting invitro culture
systems. Furthermore, NSGA-II was linked to the best
model to find the optimal level of PGRs for somatic
embryogenesis. According to the best of our knowledge,
this study is the first report of the application of SVR in
the field of plant tissue culture.
Results
Eects ofPGRs onsomatic embryogenesis
Although several investigations have focused on the
impact of auxins and cytokinins concentrations in chry-
santhemum embryogenesis, there is a lack of study on
the influence of auxins, cytokinins, nitric oxide, and their
interactions. e PGRs are essential factors in plant tis-
sue culture processes that are remarkably impacted the
somatic embryogenesis. e current study was deter-
mined the effects of 2,4-dichlorophenoxyacetic acid (2,4-
D), kinetin (KIN), sodium nitroprusside (SNP), and their
interactions on callogenesis rate (%), number of somatic
embryos per explant, and embryogenesis rate (%) of
chrysanthemum.
e results of this study showed that leaf explants in
the medium containing both 2,4-D and KIN led to both
callogenesis and embryogenesis. On the other hand,
the medium without PGR was not able to produce calli
and embryos. After two and three weeks from cultur-
ing, the cut ends of the leaf segments produced calli and
embryos, respectively. According to Table1, high embry-
ogenesis rate and the number of somatic embryos per
explant were achieved by using SNP along with 2,4-D and
KIN, which is higher than that produced by the media
without SNP. Also, the highest callogenesis rate (100%),
embryogenesis rate (100%), and the number of somatic
embryos per explant (57.8) were observed in the com-
bination of 9.09μM 2,4-D and 4.65μM BAP along with
20μM SNP (Table1).
SVR modeling andevaluation
SVR was used for modeling the three target variables
(callogenesis rate, embryogenesis rate, and the number of
somatic embryos) based on three input variables, includ-
ing 2,4-D, KIN, and SNP.
Two machine learning algorithms, including MLP and
SVR were used for modeling and predicting target varia-
bles. R2, RMSE, and MAE of each developed model were
presented in Table2. Comparative analysis of MLP and
SVR (Table2) showed that SVR was more accurate than
MLP in all studied parameters in somatic embryogen-
esis in both training and testing sets. As can be seen in
Figs.1, 2 and 3, the regression lines demonstrated that a
good fit correlation between the predicted and observed
data of callogenesis rate, embryogenesis rate, and the
number of somatic embryos for both the training and
testing set. R2, RMSE, and MAE of SVR vs. MLP for cal-
logenesis rate were 0.93 vs. 0.89, 9.82 vs.10.03, and 1.33
vs. 1.64 during the training set, and 0.93 vs. 0. 82, 10.67
vs. 15.40, and 1.87 vs. 2.01 during testing set, respec-
tively (Table2). R2, RMSE, and MAE of SVR vs. MLP for
embryogenesis rate were 0.97 vs. 0.93, 8.47 10.00, and
0.071 vs. 1.75 during the training set, and 0.96 vs. 0. 90,
9.71 vs. 13.75, and 0.55 vs. 1.91 during testing set, respec-
tively. Also, the performance parameters for the training
set for the number of somatic embryos were R2 = 0.99
and 0.96, RMSE = 0.81 and 1.64, MAE = 0.02 and 0.06 for
SVR and MLP, respectively, and in the testing data set for
the number of somatic embryos were R2 = 0.99 and 0.91,
RMSE = 0.94 and 2.07, MAE = 0.004 and 0.021 for SVR
and MLP, respectively (Table2).
Sensitivity analysis ofthemodels
Five hundred seventy-six data points were used to deter-
mine the overall variable sensitivity ratio (VSR) for iden-
tifying the comparative rank of inputs. e results of the
sensitivity analysis were summarized in Table3. Based
on sensitivity analysis, callogenesis rate was more sensi-
tive to 2,4-D, followed by KIN, and SNP (Table3). Also,
as can be seen in Table3, 2,4-D was the most important
factor for both embryogenesis rate and the number of
somatic embryos per explant, followed by SNP and KIN.
Model optimization
NSGA-II was linked to the SVR in order to determine the
optimal level of 2,4-D, KIN, and SNP for obtaining the
highest embryogenesis rate and the maximum number of
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Hesamietal. Plant Methods (2020) 16:112
Table 1 Eects of 2,4-D, KIN, and SNP on callogenesis rate, number of somatic embryos, and embryogenesis rate
ofchrysanthemum ofchrysanthemum
2,4-D (μM) Kin (μM) SNP (μM) Callogenesis rate (%) Embryogenesis rate (%) Embryo number
0 0 0 0.00 ± 0.00 0.00 ± 0.00 0.00 ± 0.00
4.54 0 0 84.44 ± 5.56 0.00 ± 0.00 0.00 ± 0.00
9.09 0 0 93.33 ± 3.33 0.00 ± 0.00 0.00 ± 0.00
13.63 0 0 100.00 ± 0.00 0.00 ± 0.00 0.00 ± 0.00
0 4.65 0 0.00 ± 0.00 0.00 ± 0.00 0.00 ± 0.00
4.54 4.65 0 80.00 ± 4.71 48.89 ± 5.88 4.48 ± 0.34
9.09 4.65 0 100.00 ± 0.00 100.00 ± 0.00 31.71 ± 0.74
13.63 4.65 0 100.00 ± 0.00 71.11 ± 5.88 9.02 ± 0.34
0 9.29 0 22.22 ± 7.78 0.00 ± 0.00 0.00 ± 0.00
4.54 9.29 0 91.11 ± 4.84 73.33 ± 5.77 7.69 ± 0.24
9.09 9.29 0 100.00 ± 0.00 100.00 ± 0.00 21.73 ± 0.44
13.63 9.29 0 100.00 ± 0.00 100.00 ± 0.00 4.23 ± 0.30
0 13.94 0 24.44 ± 8.01 0.00 ± 0.00 0.00 ± 0.00
4.54 13.94 0 97.78 ± 2.22 60.00 ± 6.67 6.93 ± 0.24
9.09 13.94 0 100.00 ± 0.00 86.67 ± 4.71 13.01 ± 0.36
13.63 13.94 0 100.00 ± 0.00 100.00 ± 0.00 4.06 ± 0.24
0 0 10 0.00 ± 0.00 0.00 ± 0.00 0.00 ± 0.00
4.54 0 10 88.89 ± 4.84 0.00 ± 0.00 0.00 ± 0.00
9.09 0 10 95.56 ± 2.94 0.00 ± 0.00 0.00 ± 0.00
13.63 0 10 100.00 ± 0.00 0.00 ± 0.00 0.00 ± 0.00
0 4.65 10 0.00 ± 0.00 0.00 ± 0.00 0.00 ± 0.00
4.54 4.65 10 91.11 ± 4.84 62.22 ± 7.03 5.96 ± 0.39
9.09 4.65 10 100.00 ± 0.00 100.00 ± 0.00 35.60 ± 0.69
13.63 4.65 10 100.00 ± 0.00 86.67 ± 4.71 9.87 ± 0.36
0 9.29 10 31.11 ± 6.76 0.00 ± 0.00 0.00 ± 0.00
4.54 9.29 10 95.56 ± 4.44 86.67 ± 4.71 8.82 ± 0.29
9.09 9.29 10 100.00 ± 0.00 100.00 ± 0.00 25.86 ± 0.63
13.63 9.29 10 100.00 ± 0.00 100.00 ± 0.00 5.51 ± 0.26
0 13.94 10 33.33 ± 7.45 0.00 ± 0.00 0.00 ± 0.00
4.54 13.94 10 100.00 ± 0.00 75.56 ± 4.44 7.77 ± 0.20
9.09 13.94 10 100.00 ± 0.00 100.00 ± 0.00 16.79 ± 0.37
13.63 13.94 10 100.00 ± 0.00 100.00 ± 0.00 5.28 ± 0.19
0 0 20 0.00 ± 0.00 0.00 ± 0.00 0.00 ± 0.00
4.54 0 20 95.56 ± 2.94 2.22 ± 2.22 0.22 ± 0.22
9.09 0 20 100.00 ± 0.00 4.44 ± 2.94 0.33 ± 0.24
13.63 0 20 100.00 ± 0.00 0.00 ± 0.00 0.00 ± 0.00
0 4.65 20 13.33 ± 7.45 8.89 ± 4.84 0.73 ± 0.37
4.54 4.65 20 100.00 ± 0.00 84.44 ± 5.56 9.56 ± 0.21
9.09 4.65 20 100.00 ± 0.00 100.00 ± 0.00 57.80 ± 0.21
13.63 4.65 20 100.00 ± 0.00 100.00 ± 0.00 17.07 ± 0.29
0 9.29 20 46.67 ± 5.77 13.33 ± 4.71 0.81 ± 0.30
4.54 9.29 20 100.00 ± 0.00 100.00 ± 0.00 11.64 ± 0.19
9.09 9.29 20 100.00 ± 0.00 100.00 ± 0.00 29.08 ± 0.26
13.63 9.29 20 100.00 ± 0.00 100.00 ± 0.00 7.38 ± 0.20
0 13.94 20 57.78 ± 7.03 17.78 ± 5.21 0.78 ± 0.22
4.54 13.94 20 100.00 ± 0.00 95.56 ± 2.94 11.38 ± 0.26
9.09 13.94 20 100.00 ± 0.00 100.00 ± 0.00 25.63 ± 0.42
13.63 13.94 20 100.00 ± 0.00 100.00 ± 0.00 8.60 ± 0.34
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Hesamietal. Plant Methods (2020) 16:112
somatic embryos per explant. e results of the optimi-
zation process were presented in Table4 and Fig.4. As
can be seen in Table4, the highest embryogenesis rate
(99.09%) and the maximum number of somatic embryos
per explant (56.24) can be obtained from a medium con-
taining 9.10μM 2,4-D, 4.70μM KIN, and 18.73μM SNP.
Validation experiment
According to the validation experiment, the differences
between biological validation data and predicted data via
SVR-NSGA-II were not significant (Table5). Indeed, the
optimized level of PGRs (9.10 μM 2,4-D, 4.70μM KIN,
and 18.73μM SNP) led to the highest embryogenesis rate
(100%) and the maximum number of somatic embryos
per explant (57.86) which is negligibly higher than the
predicted result. erefore, it can be concluded that
SVR-NSGA-II can be employed for accurately predicting
and optimizing plant tissue culture processes.
Discussion
Being successful in in vitro somatic embryogenesis
depends on different factors such as the composition of
the medium, gelling agents, light and temperature con-
ditions, and the application of specific combinations of
PGRs [1, 13–16, 63]. However, optimizing these factors is
time and cost consuming. Also, somatic embryogenesis is
a highly complex and nonlinear process. erefore, there
is a dire need to employ robust nonlinear computational
methods for optimizing embryogenesis parameters. e
efficiency of a good statistical approach depends on the
neat understanding of the variable structure, experi-
mental design, and using the appropriate model [64].
One of the most important primary requirements to
identify suitable statistical approaches is comprehend-
ing the type of data [65]. Variables can be clustered into
two groups, including quantitative (continuous and dis-
crete) and qualitative (ordinal and nominal). Names
Table 1 (continued)
2,4-D (μM) Kin (μM) SNP (μM) Callogenesis rate (%) Embryogenesis rate (%) Embryo number
0 0 40 0.00 ± 0.00 0.00 ± 0.00 0.00 ± 0.00
4.54 0 40 97.78 ± 2.22 0.00 ± 0.00 0.00 ± 0.00
9.09 0 40 100.00 ± 0.00 2.22 ± 2.22 0.22 ± 0.22
13.63 0 40 100.00 ± 0.00 0.00 ± 0.00 0.00 ± 0.00
0 4.65 40 17.78 ± 6.19 8.89 ± 3.51 0.44 ± 0.18
4.54 4.65 40 100.00 ± 0.00 77.78 ± 5.21 8.06 ± 0.13
9.09 4.65 40 100.00 ± 0.00 100.00 ± 0.00 45.77 ± 0.33
13.63 4.65 40 100.00 ± 0.00 100.00 ± 0.00 14.54 ± 0.20
0 9.29 40 31.11 ± 4.84 11.11 ± 4.84 0.44 ± 0.18
4.54 9.29 40 100.00 ± 0.00 100.00 ± 0.00 8.83 ± 0.18
9.09 9.29 40 100.00 ± 0.00 100.00 ± 0.00 24.74 ± 0.18
13.63 9.29 40 100.00 ± 0.00 100.00 ± 0.00 6.58 ± 0.17
0 13.94 40 68.89 ± 5.88 11.11 ± 3.51 0.56 ± 0.18
4.54 13.94 40 100.00 ± 0.00 93.33 ± 3.33 10.60 ± 0.14
9.09 13.94 40 100.00 ± 0.00 100.00 ± 0.00 21.32 ± 0.28
13.63 13.94 40 100.00 ± 0.00 91.11 ± 3.51 7.59 ± 0.18
Values in each column represent mean ± standard error
Table 2 Statistics ofMLP and SVR models forcallogenesis rate, number of somatic embryos, and embryogenesis rate
ofchrysanthemum intraining andtesting process
Model Item Callogenesis rate Embryogenesis rate Embryo number
Training Testing Training Testing Training Testing
SVR R20.928 0.928 0.966 0.956 0.996 0.994
RMSE 9.822 10.697 8.474 9.715 0.813 0.942
MAE 1.327 1.871 0.071 0.555 0.018 0.004
MLP R20.893 0.824 0.927 0.905 0.961 0.912
RMSE 10.029 15.403 10.003 13.747 1.645 2.073
MAE 1.644 2.012 1.746 1.908 0.061 0.021
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Hesamietal. Plant Methods (2020) 16:112
with two or more classes without a hierarchical order
are categorized as nominal variables, while ordinal data
have distinct order (level X is more intense than level
Y) [65, 66]. Counts that include integers are classified as
discrete data, while measurements along a continuum,
which could be included smaller fractions, are catego-
rized as continuous variables [67]. Plant tissue culture
data can be categorized as ordinal (callus quality rated as
weak, moderate, and good), nominal (callus types such as
embryogenic and non-embryogenic callus), continuous
(embryogenesis rate), and discrete (number of somatic
embryos). Traditional linear methods such as regres-
sion and ANOVA must be just applied with continuous
variables that demonstrate a linear relationship between
the explanatory and dependent variables [52, 68]. On
the other hand, invitro culture systems are considered
Fig. 1 Scatter plot of model predicted vs. observed data of chrysanthemum callogenesis rate for PGRs adjustment obtained by SVR model. a
Training set (n = 432). b Testing set (n = 144)
Fig. 2 Scatter plot of model predicted vs. observed values of chrysanthemum embryogenesis rate for PGRs adjustment obtained by SVR model. a
Training set (n = 432). b Testing set (n = 144)
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Hesamietal. Plant Methods (2020) 16:112
as complex biological systems that multiple factors can
affect the system in nonlinear ways. Hence, the conven-
tional computational approaches are not appropriate for
analyzing plant tissue culture data [65]. Recently, dif-
ferent machine learning algorithms such as neural net-
works [34, 46, 47], fuzzy logic [7, 69], and decision trees
[70, 71] have been successfully employed for predicting
and optimizing various invitro culture processes. Many
studies [35, 44, 46, 72] used MLP to predict the optimal
invitro conditions for different plant tissue culture sys-
tems. However, they only applied the MLP model and did
not compare this common algorithm with other models.
Another promising computational method not previ-
ously employed in invitro data analyses is the SVR. In
the current study, MLP and SVR, for the first time, were
used to develop a suitable model for chrysanthemum
somatic embryogenesis and compare their prediction
accuracy. According to our results, SVR had more accu-
racy than MLP for modeling and predicting the system.
Although there is no report regarding the application of
SVR in plant tissue culture, in line with our results, com-
parative studies in other fields revealed the better per-
formance of SVR in comparison to ANNs such as MLP
[57–59]. On the other hand, one of the weaknesses of
using machine learning algorithms is that it is hard to
obtain an optimized solution [52]. To tackle this problem,
several studies [25, 28, 30, 31, 34] used GA to optimize
in vitro culture conditions. However, plant tissue cul-
ture consists of different functions that sometimes they
show conflict interaction. Hence, GA, as a single objec-
tive function, cannot optimize multi-objective function
[7]. erefore, it is necessary to employ multi-objective
optimization algorithms such as NSGA-II. In the current
study, NSGA-II was linked to SVR as the most suitable
model for the optimization process. After predicting and
optimizing somatic embryogenesis via SVR-NSGA-II, the
predicted-optimized results were experimentally tested.
Based on our results, SVR-NSGA-II can be considered
as an efficient computational methodology for predicting
and optimizing different plant tissue culture systems.
Fig. 3 Scatter plot of model predicted vs. observed values of number of chrysanthemum somatic embryos for PGRs adjustment obtained by SVR
model. a Training set (n = 432). b Testing set (n = 144)
Table 3 Importance of PGRs for callogenesis rate,
number of somatic embryos, and embryogenesis rate
ofchrysanthemum according tosensitivity analysis
Output Item 2,4-D KIN SNP
Callogenesis rate VSR 4.10 1.94 1.49
Rank 1 2 3
Embryogenesis rate VSR 5.86 2.30 5.69
Rank 1 3 2
Number of somatic embryos VSR 100.33 98.93 99.04
Rank 1 3 2
Table 4 Optimizing PGRs according to optimization
process via SVR-NSGAII for embryo number
andembryogenesis rate inchrysanthemum
input variable (μM) Predicted
embryogenesis rate Predicted embryo
number
2,4-D KIN SNP
9.10 4.70 18.73 99.09 56.23
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Page 8 of 15
Hesamietal. Plant Methods (2020) 16:112
e results of the sensitivity analysis showed that 2,4-D
is the most important component in the somatic embryo-
genesis followed by SNP as a donor nitric oxide (NO), and
KIN. In line with our results, after several years of molec-
ular and biological somatic embryogenesis studies, it has
been shown that 2,4-D is the most important signaling
in somatic embryogenesis followed by NO and cytokinin
signaling [73]. e type and concentration of PGRs play a
pivotal role in somatic embryogenesis. Several studies [1,
14, 74] have elucidated that among tested auxins, 2,4-D
as one of the synthetic auxins resulted in the maximum
somatic embryogenesis in chrysanthemum. In addition,
kinetin, as a cytokinin, promotes somatic embryogenesis
in the chrysanthemum [75, 76]. For instance, Shinoyama
et al. [75] reported that the maximum number of the
somatic embryos (21.3 ± 1.2) was obtained from 2mg/l
2,4-D along with 1mg/l kinetin. Nitric oxide is known
as a messenger molecule regulating plant development
and a ubiquitous bioactive molecule mainly contributed
to various plant developmental processes such as fruit
ripening, flowering, organ senescence, and germina-
tion [73]. is molecule has recently been characterized
as one of the phytohormones [77]. e exterior usage
of nitric oxide might improve the tolerance of plants
under various stresses such as temperature, heavy met-
als, ultraviolet radiation, drought, and salinity [78–80].
e activation rate of nitric oxide has been evaluated by
the exterior usage of sodium nitroprusside (SNP) instead
of using NO gas directly because of some technical dif-
ficulties [81]. In recent years, nitric oxide gets involved in
developing invitro plant propagation [82]. Ötvös etal. [9]
demonstrated that despite NO does not affect cell cycle
progression in plant tissue culture, it may have a close
relation with auxins linking the adjust of cell division to
differentiation. Plants have significant developmental
plasticity in comparison with animals. During the de- dif-
ferentiation process, somatic plant cells can repossess the
ability to divide and ‘de-differentiated’ plant cells can ‘re-
differentiate’ into whole plants under appropriate condi-
tions. Ötvös etal. [9] reported that NO accompany with
auxin can play a significant role in the embryogenesis of
leaf protoplast-derived cells. In the absence of auxin, SNP
Fig. 4 Pareto front obtained by NSGA‑II as a multi‑objective optimization algorithm for the highest of embryogenesis rate and the maximum
number of somatic embryos per explant of chrysanthemum. The ideal point is presented as the red point
Table 5 Experimental validation of the predicted-
optimized result via SVR-NSGA-II for embryo number
andembryogenesis rate ofchrysanthemum
Treatment Embryogenesis rate (%) Embryo number
9.1 μM 2,4‑D + 4.7 μM
KIN + 18.73 μM SNP 100 ± 0.00 57.86 ± 0.42
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Page 9 of 15
Hesamietal. Plant Methods (2020) 16:112
could not induce the protoplast-derived cells division.
Also, the alternative response of protoplast-derived cells
to various concentrations of external auxin in the pres-
ence of SNP or L-NMMA may show that NO can alter
the sensitivity of the cells to auxin and involved in inter-
mediary of the auxins role during these processes [8].
Furthermore, NO and auxins were suggested to share
similar steps in signal transduction pathways caused to
root formation and root elongation [73]. In addition to
affecting the dividing cells frequency, SNP and L-NMMA
have a massive impact on the pathway of auxin con-
centration-dependent development of leaf protoplast
obtained from cells [73]. It previously indicated that
these cells could develop into elongated cells or small,
vacuolized, and isodiametric cells with dense cytoplasm
showing embryogenic competence [83–85]. Although
the formation of embryo-genic-type cells can be obtained
at the high concentration of auxins (5–10μM 2,4-D), by
using SNP, this type of cell can be achieved at a low con-
centration of 2,4-D [9]. Somatic embryo formation can
be obtained by the high-level expression of the MsSERK1
gene as well as the development of the cells [86] so this
fact proved the usage of SNP in altering the pathway of
the auxin-treated cells. SERK gene expression is usually
applied as a marker of embryogenic potential [73] despite
its up-regulated expression. is was also accompanying
with auxin-promoted root formation [86] and was rec-
ommended to be morphogenic instead of only being an
embryogenic marker.
Conclusion
Recently, MLP has been widely applied for modeling
and predicting in vitro culture systems. In the cur-
rent study, SVR for the first time was applied to model
and predict somatic embryogenesis and to compare its
accuracy with MLP. Our results showed that the SVR
model has better accuracy than MLP for modeling and
predicting complex systems such as somatic embryo-
genesis. Also, SVR-NSGA-II was able to optimize the
chrysanthemum’s somatic embryogenesis accurately.
e results of the sensitivity analysis showed that
2,4-D is the most important component in the somatic
embryogenesis followed by SNP as a donor nitric oxide
(NO), and KIN. Interestingly, after several years of
molecular and biological somatic embryogenesis stud-
ies, it has been shown that 2,4-D is the most important
signaling in somatic embryogenesis followed by NO
and cytokinin signaling. ese results demonstrate that
SVR-NSGA-II can open a reliable and accurate window
to a comprehensive study of the plant’s biological pro-
cesses. It would be recommended to compare SVR with
the current machine-learning methods (e.g., Random
Forest, Gradient Boosting), to allow a more thorough
appreciation of the relative merit of SVM applied to the
presented problem.
Methods
Plant material, media, andculture condition
In this study, leaf explants of chrysanthemum ‘Hornbill
Dark’ were selected for invitro somatic embryogenesis
study. To primary disinfect, the explants were washed
for 20min with tap water. en, further steps were per-
formed under a laminar airflow cabinet. Subsequently,
the explants were soaked with 70% ethanol for 40s and
then washed with sterilized distilled water for 3 min.
Afterward, the explants dipped in 1.5% (v/v) NaOCl solu-
tion for 15min. Subsequently, the explants were washed
with sterilized distilled water for 5min three times. e
basal medium in this study was Murashige and Skoog
[87] (MS) medium consisted of 3% sucrose, 0.7% agar,
and 100mg/l Myo-inositol. Also, the pH of the medium
by using 1 and/or 0.1N NaOH as well as 1 and/or 0.1N
HCl was adjusted to 5.8 before autoclaving for 20 min
at 120 ◦C. e explants were cultured in 200-ml culture
boxes supplemented with 45ml basal media. All culture
boxes were kept in the growth chamber under 16-h Pho-
toperiod with 50μmolm−2s−1 light intensity at 25 + 2°C.
Experimental design
e leaf explants were cultured in the basal medium
containing different concentrations of 2,4-D, (0, 4.54,
9.09, and 13.63μM) Kinetin (KIN) (0, 4.65, 9.29, and
13.94μM), and sodium nitroprusside (SNP) (0, 10, 20,
and 40μM). e callogenesis rate (Eq.1), embryogen-
esis rate (Eq.2), and the number of somatic embryos
were calculated after 6weeks of culture.
e somatic embryogenesis experiments were con-
ducted based on a randomized complete block design
(RCBD) with a factorial arrangement with a total of 64
treatments with nine replications per treatment, and
each replication consisted of five leaf explants.
(1)
Callogenesis rate (%)
=
Number of explants that produce callus
Total number of explants
×100
(2)
Embryogenesis rate (%)
=
Number of explants that produce embryo
Total number of explants
×100
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Page 10 of 15
Hesamietal. Plant Methods (2020) 16:112
Modeling procedures
e input variables were 2,4-dichlorophenoxyacetic acid
(2,4-D), kinetin (KIN), sodium nitroprusside (SNP). e
target variables were callogenesis rate, embryogenesis
rate, and the number of the somatic embryos per explant.
Before modeling, the datasets were scaled between 0 and
1 to ensure that all variables receive equal attention dur-
ing the training process. In the current study, two types
of machine learning algorithms, including MLP and SVR,
were employed to model somatic embryogenesis of chry-
santhemum. To train and test each model, 70 and 30% of
the data lines were randomly selected, respectively.
Multilayer perceptron (MLP) model
e MLP, as one of the common ANNs, consists of three
layers, including input, hidden, and output. In the present
study, this model was employed, according to Hesami
et al. [35] procedure. Briefly, in the present investiga-
tion, a 3-layer backpropagation network (feed-forward
backpropagation) was applied for constructing the MLP
model. To determine the optimal weights and bias as well
as train the network, a Levenberg–Marquardt algorithm
was applied. Also, the hyperbolic tangent sigmoid (tan-
sig) and linear (purelin) activation functions were utilized
for hidden and output layers, respectively.
Support vector regression (SVR) model
Support vector machines (SVMs), developed by Vap-
nik [53], can be used for clustering, classification, and
regression analysis of nonlinear relationships [54]. SVR,
as a regression version of SVM, was employed in the cur-
rent study. Considering
{
(
xi,ti
)
}n
i
as a dataset, xi shows ith
input vector, ti represents ith output vector, and n equals
a total number of observations. e following function
used for the SVR estimation:
where w shows weights, b is bias, and
ϕ(x)
represents
the high dimensional feature space, which is non-lin-
early mapped from the input space x and y is output
value. SVR tried to minimize a loss function, and the
main goal is that all the estimated variables are placed
between the upper and lower prediction error bounds.
Upper and lower prediction error bounds in SVR are
y=wϕ(x)+b+ε
and
y=wϕ(x)+b−ε
, resp ectively.
Figure5 shows a schematic view of SVR. An optimiza-
tion process was used to find out w and b coefficients as
follows:
(3)
y=w
ϕ(
x
)
+b
(4)
Min :L=C1
n
n

i=1
Lε(ti,yi)+1
2w.wT
where,
ε
,
Lε
, and C represents an acceptable error (tube
size), insensitive loss function, and penalty parameter,
respectively. Both and C are user-prescribed parameters.
e dual function of the problem with the application of
Lagrange multipliers is as follows:
After solving the optimization problem, w and b are
determined. e lagrange multipliers with non-zero val-
ues were assumed as the supporting vector. en the
SVR can be carried out as follows:
Among the various kernel functions in SVR, radial basis
function (RBF) is one of the common kernel functions for
nonlinear problems. erefore, SVR along with RBF ker-
nel function could be presented with three parameters as
SVR (y, C, Ɛ).
Performance measures
To assess and compare the accuracy of mentioned mod-
els, three following performance measures including R2
(coefficient of determination), Root Mean Square Error
(RMSE), and Mean Absolute Error (MAE) were used:
(5)
L
ε(ti,yi)=
|t−y|−ε|t−y|>ε
0otherwise
(6)
Max LD=
n

i=1
ti(αi−α∗
i)−ε
n

i=1
(αi+α∗
i)
−1
2
n

i=1
n

j=1
(αi−α∗
i)(αj−α∗
j)k(xi,xj
)
Subjected to :
n

i=1
(αi−α∗
i)=0
0≤αi≤Ci=1, 2, ...,n
0≤α∗
i
≤Ci=1, 2, ...,n
(7)
y=
n

i=1
(αi−α∗
i)k(x,xi)+
b
(8)
R
2=



T
t=1yt−¯yˆyt−ˆ
¯y

T
t=1

yt−¯y

T
t=1

ˆyt−ˆ
¯y





2
(9)
MAE =1/n
n

i=1


yi−ˆyi


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Page 11 of 15
Hesamietal. Plant Methods (2020) 16:112
where yt,
¯y
,
ˆyt
, and T are the tth observed data, the mean
of observed values, the mean of predicted values, and
total number of predicted values, respectively. Greater
R2 and smaller RMSE and MAE indicated better perfor-
mance of the constructed models.
Optimization ofsomatic embryogenesis viaNSGA-II
To identify the optimal levels of inputs (2,4-D, KIN, and
SNP) for maximizing embryogenesis rate and the number
of the somatic embryo per explant, the developed SVR
models were exposed to NSGA-II (Fig. 6). Also, a rou-
lette wheel selection method was applied to choose the
elite population for crossover [88]. To obtain the best fit-
ness, the initial population, generation number, mutation
(10)
RMSE
=

n
i=1

yi−ˆyi

2

/
n
rate, and crossover rate were respectively adjusted to 200,
1000, 0.5, and 0.7. In the current study, the ideal point
of Pareto was selected such that embryogenesis rate and
the number of somatic embryos per explant became
the maximum. Indeed, a point in the Pareto front was
detected as the best optimal answer such that:
Was minimal; where x and y were the highest embryo-
genesis rate and the maximum number of somatic
embryos per explant in observed data, respectively
Sensitivity analysis
Sensitivity analysis was conducted to identify the impor-
tance degree of KIN, SNP, and 2,4-D on the embryogen-
esis rate, callogenesis rate, and the number of the somatic
embryo per explant. e sensitivity of these parameters
was measured by the criteria including variable sensitivity
error (VSE) value displaying the performance (root mean
(11)

embryogenesis rate −x

2+

number of somatic embryos per explant −y
2
Fig. 5 The schematic view of the support vector regression (SVR) model
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Page 12 of 15
Hesamietal. Plant Methods (2020) 16:112
square error (RMSE)) of SVR-NSGA-II model when that
input variable is removed from the model. Variable sen-
sitivity ratio (VSR) value was determined as the ratio of
VSE and SVR-NSGA-II model error (RMSE value) when
all input variables are available. A higher important vari-
able in the model was detected by higher VSR.
MATLAB (Matlab, 2010) software was employed to
write codes and run the models.
Validation experiments
In order to approve the efficiency of the developed
model, the optimized PGRs (medium containing 9.10μM
2,4-D, 4.70μM KIN, and 18.73μM SNP) obtained from
SVR-NSGA-II were experimentally tested in the lab with
three replications and each replication consisted of ten
leaf explants. e obtained experimental results were
compared with predicted results.
Acknowledgements
Not applicable.
Authors’ contributions
MH performing the experiments, data modeling, summing up, and writing the
manuscript. RN and MT Designing and leading the experiments and revising
the manuscript. MYN Revising the manuscript. All authors read and approved
the final manuscript.
Funding
There were no available funding resources for this manuscript.
Availability of data and materials
All data generated or analysed during this study are included in this published
article.
Ethics approval and consent to participate
Not applicable.
Consent for publication
Not applicable.
Competing interests
The authors declare that they have no competing interests.
Author details
1 Department of Plant Agriculture, University of Guelph, Guelph, ON, Canada.
2 Department of Horticultural Science, Faculty of Agriculture, University
Selection
Calculate
congestion
Non-
dominated
sorting
Calculate
fitness
Population
initializatio
n
Start
End Gen> Genmax
Calculate
congestion
Non-
dominated
sorting
Calculate
fitness Mixing
Crossover
Mutation
Gen=
Gen+1
Fig. 6 The schematic diagram illustrating optimization process via Non‑dominated Sorting Genetic Algorithm‑II (NSGA‑II)
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Page 13 of 15
Hesamietal. Plant Methods (2020) 16:112
of Tehran, Karaj, Iran. 3 Department of Plant Biotechnology, Faculty of Science
and Biotechnology, Shahid Beheshti University, G.C., Tehran, Iran.
Received: 12 May 2020 Accepted: 8 August 2020
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